Popularly called as beach, crazy night state, Goa lies on the konkan region which is filled with white sands, casurina trees, with some best clubs, and lot of history from ancient texts. North Goa is full of tourist beaches while south Goa is full of resorts to relax. Andaman is a land of virgin islands, turquoise blue waters, with Port Blair as its capital, Havelock and Neil islands are popular making it a must to visit. Being a beach territory water sports is popular where history prevails from palaeolithic age. I would prefer travel to Goa for the variety beaches, awesome cuisine and shop in the flea markets.
Goa is meant more for people who like a social, party vibe with tourists from around the world. It's also more affordable and accessible. You'll also find many things to do in Goa beyond beaches. Andaman would be an ideal vacation for peace seekers who really want to explore peaceful and pristine beaches. Andaman would be more expensive but it also offers a better location for water sports like Scuba Diving.